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Hypercube Graph
  • Difficulty Level : Basic
  • Last Updated : 05 Feb, 2019

You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Hypercube graph of order n.

Examples:

Input : n = 3
Output : 8

Input : n = 2
Output : 4

In hypercube graph Q(n), n represents the degree of the graph. Hypercube graph represents the maximum number of edges that can be connected to a graph to make it an n degree graph, every vertex has same degree n and in that representation, only a fixed number of edges and vertices are added as shown in the figure below:

All hypercube graphs are Hamiltonian, hypercube graph of order n has (2^n) vertices, , for input n as the order of graph we have to find the corresponding power of 2.

C++

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// C++ program to find vertices in a hypercube 
// graph of order n
#include <iostream>
using namespace std;
  
// function to find power of 2
int power(int n)
{
    if (n == 1)
        return 2;
    return 2 * power(n - 1);
}
  
// driver program
int main()
{
    // n is the order of the graph
    int n = 4;
    cout << power(n);
    return 0;
}

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Java

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// Java program to find vertices in 
// a hypercube graph of order n 
class GfG
{
  
    // Function to find power of 2 
    static int power(int n) 
    
        if (n == 1
            return 2
        return 2 * power(n - 1); 
    
      
    // Driver program 
    public static void main(String []args)
    {
          
        // n is the order of the graph 
        int n = 4;
        System.out.println(power(n));
    }
}
  
// This code is contributed by Rituraj Jain

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Python3

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# Python3 program to find vertices in a hypercube 
#  graph of order n
  
# function to find power of 2
def power(n):
    if n==1:
        return 2
    return 2*power(n-1)
  
  
# Dricer code
n =4
print(power(n))
  
  
# This code is contributed by Shrikant13

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C#

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// C# program to find vertices in 
// a hypercube graph of order n 
using System;
  
class GfG
{
  
    // Function to find power of 2 
    static int power(int n) 
    
        if (n == 1) 
            return 2; 
        return 2 * power(n - 1); 
    
      
    // Driver code 
    public static void Main()
    {
          
        // n is the order of the graph 
        int n = 4;
        Console.WriteLine(power(n));
    }
}
  
// This code is contributed by Mukul Singh

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PHP

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<?php
// PHP program to find vertices in 
// a hypercube graph of order n 
{
  
    // Function to find power of 2 
    function power($n
    
        if ($n == 1) 
            return 2; 
        return 2 * power($n - 1); 
    
      
    // Driver Code
    {
          
        // n is the order of the graph 
        $n = 4;
        echo(power($n));
    }
}
  
// This code is contributed by Code_Mech
?>

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Output:

16

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